Cyclotron Resonance in Bilayer Graphene

We present the first measurements of cyclotron resonance of electrons and holes in bilayer graphene. In magnetic fields up to $B=18\mathrm{T}$, we observe four distinct intraband transitions in both the conduction and valence bands. The transition energies are roughly linear in $B$ between the lowest Landau levels, whereas they follow $\sqrt{B}$ for the higher transitions. This highly unusual behavior represents a change from a parabolic to a linear energy dispersion. The density of states derived from our data generally agrees with the existing lowest order tight binding calculation for bilayer graphene. However, in comparing data to theory, a single set of fitting parameters fails to describe the experimental results.

Figure 1

Representative traces showing normalized IR transmission data. In each, the resonance dip is due to the CR transition at filling factor $\nu =-8$ for $B=18\mathrm{T}$, $\nu =12$ for 14 T, and $\nu =16$ for 10 T, while the resonance peak corresponds to the CR at $\nu =\pm 4$ of the normalizing scans. White overlay traces are best Lorentzian fits, with arrows indicating dip and peak positions. The traces are offset vertically. Upper left inset: quantum Hall effect of bilayer graphene sample measured in situ at $B=18\mathrm{T}$. Upper right inset: schematic of the zero-field dispersion relation of bilayer graphene.

Figure 2

LL transition energies as a function of B. Open (filled) symbols represent transitions between electron (hole) LLs. Solid lines represent best fits using Eq. (2) with ${\gamma }_1=0.35\mathrm{eV}$ and the band velocity $\tilde{c}$ as a fitting parameter. Dashed lines are fits to Eq. (2) using ${\gamma }_1=0$.

Figure 3

DOS as a function of energy, derived from LL transition energies for single layer and bilayer graphene. Open (filled) symbols represent electron (hole) data. For single layer data [9], inverted triangles are $n=-1\to 0$ and $0\to 1$ LL transitions; thin diamonds are $-3\to -2$ and $2\to 3$. For bilayer data, the symbols are the same as Fig. 2. The solid line fit through the single layer data yields $\tilde{c}=1.04\times {10}^6\mathrm{m}/\mathrm{s}$. Dashed (dotted) lines are fits to the bilayer electrons (holes) yielding ${\gamma }_1=0.43\mathrm{eV}$ and 0.52 eV, respectively. For both, $\tilde{c}=1.20\times {10}^6\mathrm{m}/\mathrm{s}$. Symbols overlaid with $+(\times )$ indicate data at $B=10(16)\mathrm{T}$.